Closure to “Vertical Vibration Analysis of Suspension Bridges”

Abstract

A method of analysis is outlined for free vertical vibrations of suspension bridges. The method employs a digital computer and a finite element approach, and uses a linearized theory which restricts the amplitudes of vibrations to be small. The analysis is designed to determine the natural frequencies, modes of vibration, and energy storage capacities of the different members of the bridge. Both symmetric and antisymmetric modes of vibrations are considered. For the symmetric modes (which include additional vibrational cable tension), it is shown that it is imperative to include the elasticity of the cables if correct solutions are to be obtained. A detailed numerical example, which includes the effect of the extensibility of the cables and the elasticity of the towers, is presented and the results are examined by a comparison between measured and computed natural frequencies and mode shapes of a real bridge; the comparison shows good agreement.